What are the best statistical methods to identify anomalies in data?

2 Non-parametric methods

Non-parametric methods do not rely on any assumptions about the distribution of the data. They use techniques, such as density estimation, clustering, or rank ordering, to identify the regions or groups where most of the data points belong, and mark any data points that are isolated or distant from these regions or groups as anomalies. For example, you can use a kernel density estimation to estimate the probability density function of the data, and set a threshold to determine whether a data point has a low enough density to be an anomaly. Non-parametric methods are more flexible and robust than parametric methods, but they may require more computational resources and tuning parameters.

3 Linear models

Linear models assume that the data can be explained by a linear combination of variables or features, such as regression or principal component analysis. They use coefficients or weights to measure the contribution of each variable or feature to the data, and flag any data points that have large residuals or low scores as anomalies. For example, you can use a linear regression to fit a line to the data, and calculate the distance of each data point from the line as a measure of anomaly. Linear models are simple and fast, but they may not capture the non-linear or complex relationships in the data.

4 Non-linear models

Non-linear models assume that the data can be explained by a non-linear or complex function of variables or features, such as neural networks, support vector machines, or decision trees. They use layers, kernels, or rules to learn the function from the data, and flag any data points that have high errors or low probabilities as anomalies. For example, you can use a neural network to learn a non-linear mapping from the input to the output, and calculate the reconstruction error of each data point as a measure of anomaly. Non-linear models are powerful and versatile, but they may be prone to overfitting or underfitting, and require more data and training.

5 Hybrid models

Hybrid models combine two or more of the above methods to leverage their strengths and overcome their weaknesses. They use techniques, such as ensemble learning, feature engineering, or dimensionality reduction, to integrate different methods and models, and flag any data points that are inconsistent or contradictory as anomalies. For example, you can use a feature engineering technique to transform the data into a more suitable form for a parametric method, and then use an ensemble learning technique to combine the results of multiple parametric methods. Hybrid models are flexible and adaptive, but they may be complex and difficult to interpret.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?